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A288689
Number of n-digit biquanimous strings using digits {0,1,...,5}.
2
1, 1, 6, 46, 376, 2841, 19718, 128535, 805848, 4942711, 29970542, 180700389, 1086570460, 6525662885, 39170135870, 235062159691, 1410477973872, 8463133736523, 50779476069198, 304678570340665, 1828075815690100, 10968466276145161, 65810827526263678
OFFSET
0,3
COMMENTS
A biquanimous string is a string whose digits can be split into two groups with equal sums.
LINKS
Index entries for linear recurrences with constant coefficients, signature (23, -231, 1351, -5153, 13557, -25301, 33829, -32226, 21368, -9376, 2448, -288).
FORMULA
G.f.: (144*x^14 -1224*x^13 +4976*x^12 -11002*x^11 +18115*x^10 -25255*x^9 +30319*x^8 -29516*x^7 +21747*x^6 -11691*x^5 +4506*x^4 -1212*x^3 +214*x^2 -22*x +1) / ((6*x-1) *(3*x-1) *(2*x-1)^4 *(x-1)^6).
MATHEMATICA
CoefficientList[Series[(144x^14-1224x^13+4976x^12-11002x^11+18115x^10-25255x^9+30319x^8-29516x^7+21747x^6-11691x^5+4506x^4-1212x^3+214x^2-22x+1)/((6x-1)(3x-1)(2x-1)^4(x-1)^6), {x, 0, 40}], x] (* or *) LinearRecurrence[{23, -231, 1351, -5153, 13557, -25301, 33829, -32226, 21368, -9376, 2448, -288}, {1, 1, 6, 46, 376, 2841, 19718, 128535, 805848, 4942711, 29970542, 180700389, 1086570460, 6525662885, 39170135870}, 40] (* Harvey P. Dale, Aug 18 2025 *)
CROSSREFS
Column k=5 of A288638.
Sequence in context: A380864 A301421 A383610 * A390589 A386811 A271933
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jun 13 2017
STATUS
approved